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Nonparametric estimation for self-selected interval data collected through a two-stage approach

Angel G. Angelov () and Magnus Ekström ()
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Angel G. Angelov: USBE, Umeå University
Magnus Ekström: USBE, Umeå University

Metrika: International Journal for Theoretical and Applied Statistics, 2017, vol. 80, issue 4, 377-399

Abstract: Abstract Self-selected interval data arise in questionnaire surveys when respondents are free to answer with any interval without having pre-specified ranges. This type of data is a special case of interval-censored data in which the assumption of noninformative censoring is violated, and thus the standard methods for interval-censored data (e.g. Turnbull’s estimator) are not appropriate because they can produce biased results. Based on a certain sampling scheme, this paper suggests a nonparametric maximum likelihood estimator of the underlying distribution function. The consistency of the estimator is proven under general assumptions, and an iterative procedure for finding the estimate is proposed. The performance of the method is investigated in a simulation study.

Keywords: Informative interval censoring; Self-selected intervals; Nonparameric maximum likelihood estimation; Two-stage data collection; Questionnaire surveys (search for similar items in EconPapers)
Date: 2017
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